Q. A person wants to shoot a rocket off of a mountain 3.26 km high so that the rocket, when shot at 31.3¡Æ above the horizontal from the very top of the mountain, lands at the foot of the mountain 9.37 km (horizontal distance) away.
a) What initial speed must the rocket have? (Assume that the only force acting on the rocket after it is blasted from the top of the mountain is gravity.)
b) How long would rocket spend in the air?
I need help with this problem.
I don't know how to start this question, i know that its projectile and i can use the maxHeight and Range equation but the question only gives the height from the top of the mountain to the ground and the distance travelled.
Thank you.
Did u get the answer? im doing capa too.
To solve this problem, we can use the equations for projectile motion.
Let's start with part (a):
Step 1: Break down the given information:
- Height of the mountain = 3.26 km
- Angle above the horizontal = 31.3 degrees
- Horizontal distance traveled = 9.37 km
Step 2: Convert the given measurements to SI units:
- Height of the mountain = 3.26 km = 3260 m
- Horizontal distance traveled = 9.37 km = 9370 m
Step 3: Calculate the initial vertical velocity component:
Given that the rocket is shot at an angle of 31.3 degrees above the horizontal and assuming there is no initial vertical velocity, we can use the formula: v_y0 = v_0 * sin(theta).
So, v_y0 = v_0 * sin(31.3)
Step 4: Calculate the time of flight:
Since the only force acting on the rocket after it's blasted is gravity, we can use the formula:
- t_flight = 2 * v_y0 / g, where g is the acceleration due to gravity (9.8 m/s^2).
Step 5: Calculate the initial horizontal velocity component:
Given that the horizontal distance traveled is equal to the horizontal velocity component multiplied by the time of flight, we can use the formula:
- x = v_x0 * t_flight, where x is the horizontal distance traveled.
Since the initial horizontal velocity component remains constant throughout the motion, we have: v_x0 = x / t_flight.
Step 6: Calculate the initial velocity:
Using the initial vertical velocity component and the initial horizontal velocity component, we can find the initial velocity using the Pythagorean theorem:
- v_0 = sqrt(v_x0^2 + v_y0^2)
Now let's move on to part (b):
Step 7: Use the formula for time of flight (t_flight) obtained in step 4 to get the answer.
By following these steps and plugging in the given values, you should be able to find the initial speed (part a) and the time spent in the air (part b) for the rocket.